What is the probability that a randomly chosen resident of Town X is

IMO : D

St 1: Town X has 10,000 male residents and 15,000 female residents.

P = 15000/25000 = 3/5
Suff

St 2 : If the number of male residents of Town X were to increase by 20%, the number of male residents of Town X would be 80% of the number of female residents of Town X.

Let No. of male residents = M
Let No. of female residents = F
Thus total = M+F

Given 1.2M = 0.8F
M = 2/3 F

P = \(\frac{F}{(M+F)}\)
= 3/5
Suff

PRINCETON REVIEW OFFICIAL SOLUTION:

Statement 1 is obviously sufficient to answer the question, but Statement 2 is confusing and intimidating. The test writers are trying to get you to choose answer choice A – Statement 1 is sufficient, Statement 2 is not – and that’s exactly what most people will pick. But a smart test-taker sees the trap and guesses that there probably is a way to answer the question using Statement 2 alone, and chooses D – each statement alone is sufficient – the correct answer.

The lesson here is simple:

When you are faced with one easy statement that obviously answers the question, and one complicated statement, the complicated statement probably works, and the answer is probably D.

Wondering how to answer the question using Statement 2 alone?

Statement 2:

Remember that we’re being asked for the probability that resident of Town X is female. To solve for a probability, you don’t need the actual numbers – a percentage, ratio, or fraction will work just fine. We can write an equation with statement 1, if m represents the males and f represents the females:

m + .2m = .8f

1.2m = .8f

Divide both sides by f and by 1.2, and you get:

m/f = .8/1.2 = 8/12 = 2/3

So the ratio of males to females is 2 to 3. From there we can calculate the probability of choosing a male or a female.

(1) Town X has 10,000 male residents and 15,000 female residents.

This statement is Super easy

\(\frac{Female}{Total (Male +Female)} = \frac{15,000}{25,000} = \frac{3}{5}\)= 60%

SUFFICIENT

(2) If the number of male residents of Town X were to increase by 20%, the number of male residents of Town X would be 80% of the number of female residents of Town X.

\(Male = M\)

\(Female = F\)

\(1.2M=0.8F\)

\(12M=8F\)

\(M= \frac{8F}{12}\)

P(Females)= \(\frac{Female}{Female + Male}\)= \(\frac{F}{F+M}\) or\(\frac{F}{F+(8F/12)}\) =\(\frac{12F}{20F}\)= \(\frac{3}{5}= 60\)%

SUFFICIENT

ANSWER IS D

Are we making an assumption here that the only residents are Male and Female. What about others?
Kids for instance.

Hello

Kids also would be either male or female depending on their gender.

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